1. The sum of the digits of a two-digit number is 8. If the digits are

1.	1. The sum of the digits of a two-digit number is 8. If the digits are reversed, the new number increases by 18.Find the number.
Answer» Let the two digit number be xy x + y = 8 Right away I can logically see that, since the value increases if the digits are reversed, our choices are: 17 26 35 If I reverse 17 I get 71 .. This is more than an 18 increase If I reverse 26 I get 62 ... This is more than an 18 increase If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer ************************************* Now algebraically: x + y = 8 {equation 1} The value of xy is 10x + y The value of yx is 10y + x 10y + x = 10x + y + 18 9y - 9x = 18 9(y - x) = 18 y - x = 2 From equation 1: y = 8-x 8 - x - x = 2 8 - 2x = 2 -2x = -6 x = 3 y - x = 2 y - 3 = 2 y = 5 Originalnumber xy = 35

1. The sum of the digits of a two-digit number is 8. If the digits are reversed, the new number increases by 18.Find the number.

Answer»

Let the two digit number be xy

x + y = 8

Right away I can logically see that, since the value

increases if the digits are reversed, our choices are:

If I reverse 17 I get 71 .. This is more than an 18 increase

If I reverse 26 I get 62 ... This is more than an 18 increase

If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer

*************************************

Now algebraically:

x + y = 8 {equation 1}

The value of xy is 10x + y

The value of yx is 10y + x

10y + x = 10x + y + 18

9y - 9x = 18

9(y - x) = 18

y - x = 2

From equation 1: y = 8-x

8 - x - x = 2

8 - 2x = 2

-2x = -6

x = 3

y - x = 2

y - 3 = 2

y = 5

Originalnumber xy = 35